Design DFA for the following languages L={w |w does not contains substring ab} over ∑={a,b}


SOLUTION:

∑={a,b}

Ø  So DFA can be Q={ q0 , q1 , q2 },∑={a,b }, q0={ q0},F={ q0 , q1 } and δ is given by the table
1)Transition diagram:




   2)Transition Table:

Present State
Next State
Input a
Input b
à *q0
q1
q0
        *q1    
   q1    
q2
      q2
q2
q2

  3)Transition function:
δ( q0, a)= q1     ,δ (q0,b)= q0   
            δ( q1, a)= q1     ,δ (q1,b)= q2   
δ( q2, a)= q2     ,δ (q2,b)= q2   

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